Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry?

In this work, we attempt to characterize the main theoretical difficulties to prove the existence of competitive equilibrium in infinite dimensional models. We shall show cases in which it is not possible to prove the existence of equilibrium and some others in which, however the existence of equilibrium can be proved, the equilibrium prices seem not to have natural economic interpretation. Nevertheless in pure exchange economies, most of these difficulties may be avoided by mild restrictions on the model. In productive economies new specifics problem appear, for instance non convexity of the production sets or non boundedness of the feasible allocation sets. To prove the existence and the efficiency of the equilibrium in productive economies we need some strong hypothesis about the technological possibilities of each firm.